Green Flag, wait a few seconds for the morph to start. Keys to control the project are below the explanation. Can a Cube morph smoothly into a Dodecahedron? *********************************************************** A Cube has 6 square faces, 8 vertices and 12 edges. A Dodecahedron has 12 pentagonal faces, 20 vertices and 30 edges. Morph one to the other ... yeah, right. Split each cube face into 2 triangles and 2 trapeziums, then stretch each face into a trapezoidal wedge. At just the right height and angle, each triangle from a cube face aligns with a trapezium from another cube face to form one of the pentagonal faces of the dodecahedron ... WOO HOO! The colour schemes for the cube show the pairs of adjacent triangles and trapeziums from two adjacent cube faces that will combine to form each pentagon. <c> key to change colour schemes The first colour scheme uses one colour but a different shade for the triangle and trapezium that combine to form each pentagonal face of the dodecahedron. The second colour scheme uses the same colours, but the different shades for the triangle and trapezium merge to a single shade for the pentagon faces of the dodecahedron. <m> key to toggle between automatic and manual rotation and morphing * useful to see how it all works * While in manual mode: - use the slider to morph the cube to a dodecahedron. - use the <arrow> keys and <a> and <z> keys to rotate the object about its X,Y and Z axes. Press <m> again to return to automatic rotation.
This animation shows how 6 trapezoidal wedges can be added to a cube to form a dodecahedron: https://www.geogebra.org/m/eNXwjMD9 3D Tutorial Studio: https://scratch.mit.edu/studios/5040029/ My Polyhedrons Studio: https://scratch.mit.edu/studios/5085215/ https://en.wikipedia.org/wiki/Regular_dodecahedron Code for loading objects with different types of polyhedron faces from "3D Truncated Octahedron" https://scratch.mit.edu/projects/213509646/ Huge thanks to @TheLogFather for his "Faster Triangle Filler" https://scratch.mit.edu/projects/24828481/ 3D Rotation theory from Wikipedia: https://en.wikipedia.org/wiki/Rotation_matrix
